Welcome home my love 🤍

This is a little corner of the internet I built just for us. Somewhere to keep our memories, our distance, and my love for you. I hope this place makes you feel comfortable in some way.

Feel free to explore MrTeddy's home...

My Poems For You

Ode to my Golden One

▼

My lady,

Among the stars we may see,
I chose not to look but at you, lovely.
From the misty north of France,
I dream about a Bengali romance.

Our cruel destiny placed between us,
The nine skies and the seven seas,
Strengthening our idyllic trust,
And nurturing our dreams like trees.

Yet distance can’t dim our flame,
In my love story, I write your name.
Through the words and letters penned,
Your injured soul, I long to mend.

Your eyes, black and inspiring, shimmer,
Bending space and time, they shine.
Orbiting and shivering, they’re mine.
But distant am I, perceiving just a glimmer.

At your side, my spirit dances and flies,
Watching over you like a bird in the skies.
At your side, my heart flutters and aches,
Loving you the most, whatever it takes.

Among the flowers we may gather,
I chose your pistil, making you my lover.
From the flourishing land of Bengal,
Where dreams reach the Heaven hall.

Ô my golden princess,
In these tough times, I must confess.
Your verb first left me voiceless,
And fantasizing about a white dress.

Let’s take ourselves to the edge of the world,
Where all our ambitions unfurl.
Your complex essence, I yearn to fathom,
Bringing you to the cherry blossom.

Ô my resplendent goddess,
You are the divine cure to my illness.
I beseech you to cleanse these curses,
And bless me with thy velvet curves.

While meeting you every night,
You keep missing in the daylight.
Can you hear this gloomy melody?
The song of my heart, missing its beauty.

Ô my radiant and gleaming star,
Your charm brings me light from afar.
Your elegance heals me to the deepest scar.

Among the universes we may reach,
We reside in the favored one in which,
Your existence is intricated with mine,

My lady, I love you the most,
Offering you passion and pleasure.
My lady, you are my cherished treasure.

Together, forever, we will chuckle.

Your greatest lover, Arnaud

A Piece of Poetry for my Lover - I

▼

Dreaming in my slumber,
I see you, my adorable lover.
You and your sparkling eyes,
I will forever love, without any lies.

A Piece of Poetry for my Lover - II

▼

In the Bengali night skies,
Glow the stars, the moon and your eyes.
Every time you get into my sight,
Your majesty locks me in a prison of light.

On the French sacred land,
I put all my joy into my hand,
Getting teary for you my love
Who's my radiant and tender dove.

Love

▼

My love,

During my whole life of solitude,
I heard the flowers singing your name.
My heart beats now the song of fortitude,
And gives me the courage to declare my flame.

Will you join me in a dreamy journey?
We could walk and run far away,
Talking peacefully and bantering kindly.
We could love and care in perfect harmony.

You are my beloved princess,
The one I want by my side forever,
And giving me this feeling of success.

I feel more in love with you every day.
Demanding for your eyes more than I should,
I will cherish you more than anyone could.

Your soulmate

The Golden Queen

▼

There is this girl, alive but intangible.
She seems so close, yet unreachable.

She is like gravity,
Making my heart heavier than the world,
And attracting me through any distance.

She is a siren, MY siren.
The melody of her voice drives me insane,
Losing all sense of logic and rationality.

People from her shire call her Sonai,
But she's my golden queen.
Only mine, and as precious as gold to me.

Even the sweetest words can't describe,
Her majesty, her beauty, and her gracefulness.

She was the darkest night,
And needed a blue sky to brighten her days.
She found me, and now,

She's mine,
I'm hers,

In This Vast World...

▼

...There is a man,
Who walks among countless souls,
Yet his heart beats only for yours.

Through oceans and continents,
His love travels and flows,
Like an endless river,
Finding its way to your heart.

Doves and butterflies sing and dance
For his passion towards your beauty.
While he passionately worships
Your mind, body and face.

And in this vast world,
Where time and stars
Revolve around you,
His love will remain,
Ever choosing you,
Again and again,
Forever and ever...

Hear me

▼

In the luminous night of May,
The stars heard me and said your name,
The ropes of fate tied up over us,
And my heart opened up to your soul.

My most cherished lady,
There is no mirror in this world
That can reflect your real beauty.

Hear me losing my mind
When the night takes you away from me.
Hear my pain and my sorrow
When misery falls upon you.

My adorable golden princess,
Your charm is like a lightning
That strikes me and makes me crazy.

Hear me my heart.

My love for you shall never die.
My love for you is eternal.
My love for you will grow up everyday.

Hear me, and be mine forever.
Because my heart
Will never forget about you
And will always remain yours.

I love you.

Your soulmate

My Blossom

▼

In a mirror of water, bathed in moonlight,
A lotus flower lifts up and brightens the night.
Quiet, sensitive and radiant,
You bloom with grace, so calm and elegant.

Below the surface, strong and brave,
Your roots grow and weave inside my soul.
They wrap around my heart so tight,
And hold me close both day and night.

Upon the pond, honeyed and soft,
Your petals feel like a velvet mist.
Their gentle touch, a calm embrace,
And a soothing warmth, it is my favorite place.

Tonight, a lotus rises, majestic and pure,
Showing up, unstained by the earth below.
The Shrine whisps her name,
The name of Love, Passion and Eternity.

La Marche de l'Amour

▼

Au milieu des plantes et des fleurs,
Je pense à elle en milles couleurs.
Loin des folies et des grandeurs,
J'erre sans fin, en préservant mon cœur.

De ses doux cheveux noirs à ses tendres pieds,
Je l'aime plus que tout, elle est ma bien-aimée.
À travers ses yeux, le reflet de son âme,
Je vois le bonheur, une jolie flamme.

Continuant à marcher pour l'éternité,
Je rêve de sa peau plus chaude qu'un foyer.
Elle est mienne, drôle et d'une infinie beauté.

Un beau jour, je la marierai,
Je lui montrerai mon monde,
Et je lui offrirai ma vie.

Mon Paradis

▼

Née d'amour et de tendresse,
Elle est mon Paradis.
Sa lueur, discrète et délicate,
Enrobe mon tourmenté esprit.

Est-elle vraiment réelle ?
Bien que si parfaite,
Le doute se meurt avec mon âme.
Et bien heureuse devient ma vie.

En bon dévot je me soumets,
Face à sa majesté.
Je prie et pleure au nom du Saint-Amour.
Mais le bonheur persiste toujours.

Allez-y ! Prenez-moi pour un fou !
Elle est mon monde, mon Univers !
Ricanez ! Jasez ! Mais ignorez...

Un jour,
J'irai au Paradis.

My Heart For You

The Math Behind My Love

Just like this heart is built from math, my love for you is eternal. Let's first define the heart function:

$$ H(x,t) = -\sqrt{a^2 - x^2}\cos(kx - \omega t) + \frac{2}{3}(|x| - a) $$

where:
- $a$ is the width of the heart. It can depend on time even if the time dependency is not explicit here.
- $k$ is the space frequency. It should be high enough so we can see enough oscillations so the shape of the heart is well defined.
- $\omega$ is the time frequency defined by $\omega T = 2\pi$ with $T$ the period of the oscillations in time.

As you can see from the square root, the function $H$ is only defined on $[-a, a]$. The goal here is to extend it on $\mathbb R$ such that the global function is $C^1$ on $\mathbb R^*$. Does it sound like dark magic to you my heart? 😈🤍 Well, try to follow me a little. 🥹🤍 Let's compute the derivative of $H$:

$$\frac{dH}{dx}(x,t) = \frac{x.\cos(kx - \omega t)}{\sqrt{a^2 - x^2}} + k\sqrt{a^2 - x^2}\sin(kx - \omega t) + \frac{2}{3}\mathrm{sgn}(x)$$

We have a big problem here 😭🤍. See this square root at the denominator of the first term? Because of it, the derivative of $H$ is not defined at $x = \pm a$. Should we give up? 🥹🤍 No we won't, because I am madly in love and I want to do something pretty for my wife. 😈🤍 Instead of extending our heart function from $x=\pm a$, we will just cut it a lil on the edges, so that its derivative is finite. To do that, we consider the points $x = \pm a(1 - \varepsilon)$ with $\varepsilon \ll 1$. We then pose:

$$x_0 := a(1-\varepsilon)$$

From now on, I am going to call the "left tail" the extension $T_-$ of $H$ on $]-\infty, -x_0[$ and the "right tail" the extension $T_+$ of $H$ on $]x_0, +\infty[$. Our global function, let's call it $\mathcal H$, will therefore be defined as:

$$\mathcal H(x,t) = \left\{\begin{array}{l} T_-(x,t),\quad & x < -x_0 \\ H(x,t),\quad & -x_0 \leq x \leq x_0 \\ T_+(x,t),\quad & x_0 < x \end{array}\right.$$

Are you following my baby? 🥹🤍 As I said earlier, I want the total function, $\mathcal H$, to be $C^1$ on $\mathbb R^*$. What does that mean? It means I want $\mathcal H$ to be:
- Continuous on $\mathbb R^*$
- Differentiable on $\mathbb R^*$
- Such that its derivative is continuous on $\mathbb R^*$.

Okay but why $\mathbb R^*$ and not $\mathbb R$? Because in $H(x,t)$, there is $|x|$, and the derivative of $|x|$ is not defined at $x=0$. But this is not much of a problem when we only want a pretty result. We therefore impose the following conditions:

- Continuity at $x = -x_0$:

$$T_-(-x_0,t) = H(-x_0,t)$$

- Derivative continuous at $x = -x_0$:

$$\partial_xT_-(-x_0,t) = \partial_xH(-x_0,t)$$

- Continuity at $x = x_0$:

$$H(x_0,t) = T_+(x_0,t)$$

- Derivative continuous at $x = x_0$:

$$\partial_xH(x_0,t) = \partial_xT_+(x_0,t)$$

Did you really read until here my baby? 🥺🤍 Well here is the most difficult part actually. Because who's gonna tell us the form of $T_\pm$? Exactly, no one, maths are so hard 😭🤍. We will have to guess it somehow. That's the part of the job that took me weeks to do.

The Code


#########################################
#                                       #
#       Heart animation for my love     #
#                                       #
#########################################

# Import libraries
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
from matplotlib.animation import FFMpegWriter
import matplotlib.animation as animation

#Define parameters of the animation:

#Parameters of the oscillations:
k = 15                  #Space frequency
T = 3                   #Period
w = (2 * np.pi) / T     #Time frequency

#Size of the heart: max width = 2 * a_max * (1 - e)
a_max = 7.5
e = 0.05    #Parameters ensuring differentiability

#Shape of the tails:
mu = 10

def a_func(t):
    """
    Docstring for a_func
    
    :param t: Real value

    Allows for the width of the heart to change in time.
    """
    return a_max

def H(x,t):
    """
    Docstring for H
    
    :param x: Real value
    :param t: Real value

    Gives the heart function. Only defined on [-a, a]
    """
    a = a_func(t)
    return - np.sqrt(a**2 - x**2) * np.cos(k * x - w * t) + (2/3) * (np.abs(x) - a)

def H_deriv(x, t):
    """
    Docstring for H_deriv
    
    :param x: Real value
    :param t: Real value

    Gives the derivative of H. Only defined on ]-a, a[
    """
    a = a_func(t)
    H1 = (x / np.sqrt(a**2 - x**2)) * np.cos(k*x - w*t)
    H2 = k * np.sqrt(a**2 - x**2) * np.sin(k*x - w*t)
    H3 = np.sign(x)*(2/3)
    return H1 + H2 + H3

#Define min and max values of H(x,t)
Hmin = -(5/3) * a_max
Hmax = (a_max/3) * (np.sqrt(13) - 2)

def Tail_right(x,t):
    """
    Docstring for Tail_right
    
    :param x: Real value
    :param t: Real value

    Gives the right tail.
    """
    x0 = a_func(t) * (1 - e)
    H0 = H(x0,t)
    H1 = H_deriv(x0,t)

    A = (x0**2) * (2 * H0 + (x0/2) * (H1 + mu * H0))
    B = (x0**4) * (H0 + (x0/2) * (H1 + mu * H0))

    return ((A / (x**2)) - (B / (x**4))) * np.exp(-mu * (x - x0))

def Tail_left(x,t):
    """
    Docstring for Tail_left
    
    :param x: Real value
    :param t: Real value

    Gives the left tail.
    """
    x0 = -a_func(t) * (1 - e)
    H0 = H(x0,t)
    H1 = H_deriv(x0,t)

    A = (x0**2) * (2 * H0 + (x0/2) * (H1 - mu * H0))
    B = (x0**4) * (H0 + (x0/2) * (H1 - mu * H0))

    return ((A / (x**2)) - (B / (x**4))) * np.exp(mu * (x - x0))

def f(x,t):
    """
    Docstring for f
    
    :param x: Real value
    :param t: Real value

    Gives the whole function:
    - Left tail on ]-infinity, -a(1-e)[
    - Heart on [-a(1-e), a(1-e)]
    - Right tail on ]a(1-e), +infinity[
    """
    x0 = a_func(t) * (1 - e)

    if x < -x0:
        return Tail_left(x,t)
    elif x > x0:
        return Tail_right(x,t)
    else:
        return H(x,t)
    
def f_vec(X, t):
    """
    Docstring for f_vec
    
    :param X: Real valued numpy array
    :param t: Real value

    Vectorises the function f.
    """
    Y = np.empty_like(X)
    x0 = a_func(t) * (1 - e)

    mask_left  = X < -x0
    mask_mid   = (X >= -x0) & (X <= x0)
    mask_right = X > x0

    Y[mask_left]  = Tail_left(X[mask_left], t)
    Y[mask_mid]   = H(X[mask_mid], t)
    Y[mask_right] = Tail_right(X[mask_right], t)

    return Y

# Domain
Range = 10
X = np.arange(-Range, Range, 0.01)

# Figure
fig, ax = plt.subplots(figsize=(8, 6))  # 4:3 ratio
line, = ax.plot(X, f_vec(X, 0),color='white', lw=2)

# Dark gray background
fig.patch.set_facecolor('#2b2b2b')  # figure background
ax.set_facecolor('#2b2b2b')         # axes background

#Parameters of the axes
ax.set_xlim(-Range, Range)
ax.set_ylim(Hmin - 1, Hmax + 1)   # adjust if needed
ax.set_aspect('equal', adjustable='box')
ax.set_xticks([])
ax.set_yticks([])

# Time parameters
video_length_sec = 30        # how long the MP4 should be
fps = 60                    # frames per second in the MP4
dt = 1/fps                   # time step for your function update

frames_needed = int(video_length_sec * fps)   # total frames to generate

#Define the update function called for each frame.
def update(frame):
    t = frame * dt
    Y = f_vec(X, t)
    line.set_ydata(Y)
    return line,

#Define the animation
ani = FuncAnimation(
    fig,
    update,
    frames=frames_needed,
    interval=dt*1000,
    blit=True
)

#Display the animation
plt.show()

#Define the writer for .mp4 save.
writer = FFMpegWriter(
    fps=fps,
    metadata=dict(artist='Arnaud'),
    bitrate=1800
)

#Save as .mp4 file.
ani.save("videos/HeartAnimation.mp4", writer=writer, dpi=200)

MrTeddy's Home

Welcome home my love 🤍

My Poems For You

Ode to my Golden One

A Piece of Poetry for my Lover - I

A Piece of Poetry for my Lover - II

Love

The Golden Queen

In This Vast World...

Hear me

My Blossom

La Marche de l'Amour

Mon Paradis

Where we are

Calculating...

Daily Luck Wheel

Our Memories

My Heart For You

The Math Behind My Love

The Code

MrTeddy's Home 🧸

Welcome home my love 🤍

My Poems For You

Ode to my Golden One

A Piece of Poetry for my Lover - I

A Piece of Poetry for my Lover - II

Love

The Golden Queen

In This Vast World...

Hear me

My Blossom

La Marche de l'Amour

Mon Paradis

Where we are

Calculating...

Daily Luck Wheel

Our Memories

My Heart For You

The Math Behind My Love

The Code